Given-f-3-4-f-3-2-f-8-5-f-8-3-find-3-8-x-f-x-dx-

Question Number 135784 by benjo_mathlover last updated on 16/Mar/21

G i v e n {\begin{cases} f (3) = 4, f^{'} (3) = - 2 \\ f (8) = 5, f^{'} (8) = 3 \end{cases}

f i n d \int_{3}^{8} x f^{″} (x) d x .

Answered by Ar Brandon last updated on 16/Mar/21

\int_{3}^{8} {xf}^{″} (x) dx = {xf^{'} (x) - \int f^{'} (x) dx}_{3}^{8}

= {xf^{'} (x) - f (x)}_{3}^{8} = {8 (3) - 5} - {3 (- 2) - 4} = 29